Lists

Specific Lists

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Ordering and multiplicity matter:

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True :: Bool
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True :: Bool

Lists are homogeneous, that is, all elements should be of the same type.

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<interactive>:1:2: error:
    • No instance for (Num Bool) arising from the literal ‘1’
    • In the expression: 1
      In the expression: [1, True]

The homogeneity of lists is due to strict typing. (However, inhomogeneous lists may be replaced by homogeneous lists.)

The [13] and 13 are completely different values, they are not even comparable.

Strings

'a' :: Char

Character literals: 'a', 'ű', '\369', '\\', '\n' :: Char

"apple" :: [Char]

String literals: "apple", "\n\n", "" :: String

Strings are nothing more than just list of characters:

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"abc" :: [Char]

String a synonym for [Char].

Dotdot Expressions

There are four different forms:

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[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Integer]
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[1, 3, 5, 7, 9] :: [Integer]
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And that is also possible:

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"abcdefghijklmnopqrstuvwxyz" :: [Char]

Four Basic Operations on Lists

The length function tells the number of items in the list.

length :: [a] -> Int
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3 :: Int

The index function (!!) gets an item at an index.

(!!) :: [a] -> Int -> a
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'b' :: Char

The concatenate function (++) combines two lists. They must be of the same type.

(++) :: [a] -> [a] -> [a]
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"hello" :: [Char]

The cons function (:) adds one item to the head of the list. It must be of the same type.

(:) :: a -> [a] -> [a]
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[5, 10, 20, 3] :: [Integer]

Note: With (!!), list items are numbered from zero.

Exercise: 10, 9, 8, …, -9, -10

List the numbers from 10 to -10.

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Exercise: The nth element of an Arithmetic Sequence

What is the 113th element of the arithmetic sequence whose first two elements are 11 and 32?

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Exercises

Guess the type of the following expressions:

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Sum and Product

sum :: (Foldable t, Num a) => t a -> a
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product :: (Foldable t, Num a) => t a -> a
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Exercise: Number of Different Orderings of 10 Elements

How many ways can 10 different elements be sorted?

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Exercise: Number of Combinations

How many ways can 30 elements be chosen from 70 different elements?

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Hint: Use the div function instead of (/).

Exercises

What is more: the number of atoms in the universe, or number of orderings of 100 different elements?

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What is easier: get 5 elements out of 90 or get 6 elements out of 45?

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